1. Field of the Invention
The present invention relates to a method and apparatus for numerical calculation related to fluids such as a compressible fluid, a program for causing a computer to execute the method, and a storage medium storing the program.
2. Description of the Related Art
A numerical analysis method for a compressible fluid in general is roughly classified into an analysis method which makes much of upwinding, and an analysis method which does not make much of upwinding and designs the grid system, instead.
Recently, as an efficient and stable analysis method for compressible fluids, an AUSM (Advection Upstream Splitting Method) scheme has been proposed (refer to M. S. Liu and C. J. Steffen, Jr: A New Flux Splitting Scheme, Journal of Computational Physics, 107, 23-39 (1993), for example). According to this AUSM scheme, the pressure that causes non-linearity is dealt with separately, and the ultrasonic speed is evaluated according to the functional form of an equation of state in order to carry out pressure evaluation according to the Mach number
On the other hand, as an analysis method which does not make much of upwinding, there have been proposed a central difference scheme (central scheme) (refer to H. Nessyahu, E. Tadmor, “Non-oscillatory central differencing for hyperbolic conservation laws” Journal of Computational Physics, 87, 408-463 (1990), for example), and the CE/SE scheme (refer to S. C. Chang “The Method of Space-Time Conservation Element and Solution Element—A New Approach for Solving the Navier-Stokes and Euler Equations” Journal of Computational Physics, 119, 295-324 (1995), for example). According to these schemes, a dual grid system is used to carry out calculation in the central difference scheme, and a plurality of grid systems are used to carry out calculation in the CE/SE scheme, since a conservation law in time and space is considered.
The AUSM scheme requires evaluation of the ultrasonic speed according to the functional form of the equation of state, and the central difference scheme and the CE/SE scheme require the use of a plurality of grid systems which have large calculating loads and are liable to cause numerical diffusion.